Here’s an article that I believe is flat-out entertaining to read. It’s about philosophy, so it’s supposed to be entertaining, in any case.
Here’s the abstract:
A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science.
Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.
Here’s the background:
For almost twenty years I’ve been annoyed at many Bayesians’ lack of interest in checking models, to the extent that some Bayesians even think they’re not really even really allowed to check the fit. I’ve been wanting to write a paper on the philosophy of statistics for a long time, focusing on my synthesis of Bayesian (by way of Box, Jaynes, and Rubin) and Popperian (by way of Lakatos) ideas, but I was never clear how to start.
Then, about a year ago, someone named Harold Kincaid invited to contribute an article on Bayesian statistics for the Oxford Handbook of the Philosophy of the Social Sciences. Once I knew I was going to do this, I thought I should write this as a journal article and then have another version for the handbook.
The next step was to find a collaborator. I almost always need a collaborator. I thought of Cosma Shalizi, who seemed to know a lot more than I did about recent work in the philosophy of science (an area where my knowledge base stops around 1970). I called up Cosma and was pleasantly surprised that he said yes. I ‘m pretty sure he had a bunch of ideas of his own along similar lines, so it was a good chance to work together. A few months later, the article was done (and we submitted it to a journal). The article is much better than anything I could’ve written on my own.
I was in no hurry to blog this. I put the article on my website and Cosma posted it on Arxiv, and that seemed enough for now. But then Cosma up and posted something on his blog, so I thought I should follow suit. Despite my general reluctance to post good stuff on the weekend.